This dissertation addresses two topics related to computational systems biology. Part I of the dissertation is motivated by the search for effective treatments for ischemic stroke. Ischemia refers to an inadequate blood supply that initiates a complex set of cellular signaling pathways that ultimately determine whether brain cells survive or die. Microglia --- resident immune cells of the brain --- play an influential role in determining cell fate following stroke. One pathway of particular importance involves activation of the transcription factor nuclear factor kappaB (NF-kappaB), which controls the expression of many inflammatory and cell death related genes. A deterministic model is developed to quantitatively describe the feedback-regulated NF-kappaB signaling pathway in microglia, prompted by the inability of previously published models to correctly capture the dynamics observed from experimental data sets from microglia cells. The new model incorporates previously unmodeled dynamics of inhibitor degradation and modified kinetics for upstream kinase activation. Analysis of the model shows parameter sensitivities that strongly depend on the present phase of activation. Analysis further highlights robustness to feedback parameters, analogous to engineered systems. The model is used to analyze potential regulatory mechanisms of heat shock protein 70, known to protect cells against stroke.

The second part of the dissertation develops new computational tools for sensitivity analysis of stochastic models of biochemical networks. Sensitivity analysis studies the effects of parameter perturbations on system outputs. This can be used to identify important reactions in complex signaling networks. Sensitivity analysis in stochastic models of biological systems is limited due to high computational costs needed for many Monte Carlo simulations. The development of two new efficient stochastic sensitivity methods that significantly reduce these costs --- the common reaction path method for finite parameter perturbations, and the regularized pathwise derivative method for infinitesimal perturbations --- is presented. Both methods exploit the random time change representation of stochastic models to reduce variance of Monte Carlo estimates. The numerical algorithms presented allow straightforward implementation of the methods. Computational speedups of several orders of magnitude over existing methods are demonstrated for example problems, permitting efficient sensitivity analysis of stochastic biochemical reaction networks.